36  Introduction

This module shows how to build epidemic-network models in which the epidemic and the network feed back on each other. This becomes unavoidable as soon as we leave the closed populations of the earlier modules, where the set of nodes stayed fixed. Here people enter and leave, and their attributes change, and both of those reach back and alter the network the epidemic is running on.

We first give a general background to this feedback, and to the adjustments it forces on the temporal ERGM (TERGM) coefficients, in the slides below. We then work through the two ways the feedback arises, one tutorial for each. Both tutorials configure their open-population simulations through control.net, the function that sets the run-time options netsim uses; for the full argument-by-argument reference, see The control.net Guide in Module 9.

36.1 Slides

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36.2 What Is in This Module

Epidemic Models with Demography opens the population to vital dynamics: arrivals (births) and departures (deaths). This is the first place a partnership can end because a partner leaves the population, not only because the partnership dissolves on its own, and the first place the population size can change. Each of those forces one coefficient adjustment: the death correction in dissolution_coefs, which we set ourselves, and the network-size correction inside netsim, which is automatic. The tutorial builds up in stages: the death correction on a bare edges-only network (comparing a corrected fit against an uncorrected one), then a shrinking population on that same network, which brings in the automatic network-size correction, and finally heterogeneous risk groups where both corrections work together under disease-specific mortality.

Feedback Through Nodal Attribute Changes turns to the second source of feedback, a network term that depends on an attribute the epidemic itself changes. We use disease status and serosorting, the tendency to partner within one’s own status, so that as prevalence rises the network structure shifts underneath the epidemic.

Lab is your turn to vary the demographic rates and the mixing structure and read the consequences off the diagnostics.

36.3 Module Learning Objectives

  • Describe the sources of feedback between an epidemic and its contact network, and why an open population makes them unavoidable.
  • Distinguish the two TERGM coefficient adjustments an open population requires: the death correction, for the extra way edges end, and the network-size correction, for a changing population size.
  • Implement a network-based epidemic model with vital dynamics, applying both adjustments.
  • Implement a model with feedback that runs through a changing nodal attribute (disease status), and interpret why the network statistics no longer hold flat.